"...he wasn't and still isn't sure the Khan Academy should be a business. Because it's a nonprofit, it's able to attract all kinds of talented dreamers, many of whom work for free... Giving away effective methods for mastering the world's knowledge presents a Napster-like challenge for companies such as London-based Pearson and McGraw-Hill... 'We're seeing 70 percent on average improvement on the pre-algebra topics in those classrooms. It definitely tells us it's not derailing anything. All the indicators say that something profound looks like it's happening.' "

Khan Academy is the single biggest reason my (HS Junior) daughter didn't get stuck in summer school for math this year. Her teacher was worse than useless, and Mrs. Deadmessenger and I hadn't had to use those concepts in 20 years or more - those videos got us through.posted by deadmessenger at 9:18 AM on May 28, 2011 [4 favorites]

I love this guys stuff. I finally feel like i understand certain parts of matrix arithmetic that previously left me stumped. I wish I'd had access to year as a younger man.posted by humanfont at 9:19 AM on May 28, 2011

What makes him so different is that he stays behind the camera, has a gifted voice, and he introduces each concept through insight, or "intuition" as he calls it, as a way to understand the idea (which is typically not yet posed as a problem). He's a natural teacher.posted by Brian B. at 9:20 AM on May 28, 2011 [1 favorite]

I've been using the site to bone up on my calculus and astronomy in preparation for returning to school in the near future.

I still don't know what a matrix is or what it represents, but I'm getting much better at doing integrals and differentials.posted by runcibleshaw at 9:27 AM on May 28, 2011 [1 favorite]

What a coincidence! I was just watching one of the physics videos on the Khan Academy site with my high school aged cousin. It is wonderful that there are these resources available. I'm pretty jealous that I didn't grow up with an internet full of educational resources and information.posted by anniecat at 9:29 AM on May 28, 2011 [1 favorite]

I bet people think MIT branded stuff is for supergeniuses and too hard for the average high school or college student, so they probably feel intimidated by it.posted by anniecat at 9:30 AM on May 28, 2011 [3 favorites]

I'm a math phobic computer programmer.

Finally got up the courage to take a math class at the community college.

First, I had to pass a math assessment test, it had been almost twenty years since I took a math course.

Two months of reviewing at Kahn academy I took the assessment and got into, Intro to statistics. I would have had to start with much lower level classes, costing time and money w/o Kahn academy.

I bet people think MIT branded stuff is for supergeniuses and too hard for the average high school or college student, so they probably feel intimidated by it.

The MIT Open Course Ware materials are, for the most part, actual material used in MIT courses. OCW isn't producing new materials; they're taking the lectures, homework assignments, and exams from MIT courses and making them available online in one centralized place.

Whether people should be intimidated by that or not is a question I don't want to get into.posted by madcaptenor at 9:35 AM on May 28, 2011 [1 favorite]

Also, a common criticism of the Khan Academy videos -- and one that I share from what little bit of them I've seen -- is that even though they're free, they belong to what you might call the tutoring-industrial complex. This is, of course, true to the origin story of Khan Academy, where Khan was tutoring his younger relatives. They're meant to fill in the holes that exist when people are taught by teachers who don't have a firm grasp on the material, care too much about their research and not enough about their teaching, or just have too many damn students. They don't ask the question of why students would want or need to know these things; they're just directed towards helping people jump through hoops. Should we be jumping through hoops, or should we be trying to make education less of a circus?

I'm not joking. If I had access to this when I was in college, I wouldn't have dropped out of math.

His videos are addictive. A year or so ago, I just decided to watch some of the Calculus videos, see if I understand it. (The only math class I took in college was pre-calc, and I dropped it halfway through). I spent the next few weekends watching every one of them and doing the exercises, and he made it seem really easy. He's just spectacularly good at explaining the intuition behind all of these ideas so you just get it.

I wouldn't be surprised at all to hear that he's got 7th or 8th graders doing calculus.posted by empath at 9:43 AM on May 28, 2011 [2 favorites]

The OCW can be daunting- zip files of lecture notes, videos, online discussion groups, text file text books. Plus, the MIT brand attached to it all. The Khan Academy stuff is mainly videos if I'm not mistaken (and I might be... the last time I was on that site was about 18 months ago to bone up for a math placement exam I was taking.)

Where the OCW left me a bit overwhelmed, Khan Academy left me wondering, is this all there is? I was expecting a bit more than what there was at the time and the history videos were pretty lightweight stuff, but interesting. Just browsing their library right now, I can see it's expanded quite a lot. I might give it another shot.posted by dave78981 at 9:47 AM on May 28, 2011

I still don't know what a matrix is or what it represents

Matrices can represent lots of different things, depending on what they're being used for. A matrix is just a convenient way to organize a bunch of numbers that are related to each other.posted by empath at 9:48 AM on May 28, 2011 [1 favorite]

Where the OCW left me a bit overwhelmed, Khan Academy left me wondering, is this all there is?

The history videos are kind of meh.

There's a set of videos in the calculus section where he derives euler's identity which was pretty mindblowing to me at the time, and got me excited to learn a lot more about math and geometry.posted by empath at 9:50 AM on May 28, 2011 [1 favorite]

Matrices are everywhere. They are all around us. Even now, in this very room. You can see them when you look out your window or when you turn on your television. You can feel them when you go to work... when you go to church... when you pay your taxes. They are the world that has been pulled over your eyes to blind you from the truth. What truth? 42.posted by It's Raining Florence Henderson at 9:55 AM on May 28, 2011 [8 favorites]

Based on the many endorsements I've seen over the past several months, I'm looking forward to watching some of the math and statistics videos.

But I have to say that I'm six minutes into one of the history videos (on the 1973 coup d'état in Chile), and I don't know, it's a pretty superficial treatment of the topic. I hope this isn't really the future of education, as some like to claim.posted by cobra libre at 9:57 AM on May 28, 2011 [2 favorites]

They're meant to fill in the holes that exist when people are taught by teachers who don't have a firm grasp on the material, care too much about their research and not enough about their teaching, or just have too many damn students.

I'm not offended or anything, but having taught university math for many years when i was a graduate student, I would say many of the people who go in for tutoring are people who ultimately think they can pay their way out of failing a class, where failing means anything from an actual F to not getting an A. (In the US) they will always blame the teacher first before looking at their own weaknesses and mistakes: it gets really insulting after awhile.

The thing about Khan Academy is that he manages not to be terrible. And most online/computer math pedagogy is terrible, especially when produced by big companies like Pearson. I've been working through the basic algebra stuff with my oldest son and the "mind map"/worksheets plus the videos amount to what you would get from a decent tutor: they're not terribly insightful about the math and you can tell that he actually doesn't have a lot of experience tutoring/teaching because the videos (even for basic algebra) assume a greater facility with basic math than many university students come in with (this isn't a criticism of him.)

If anything the lauding of Khan shows just how bad professional math education is (and professional math ed is a huge field getting large grants from the federal government.)posted by ennui.bz at 10:06 AM on May 28, 2011 [2 favorites]

I didn't mean that any of those described you, or anybody else that's reading this. But these are flaws that are common to a lot of people.

The thing about Khan Academy is that he manages not to be terrible.

And this is enough? Not being terrible? I guess it's a start.

I mean, teaching is hard. I teach college math, I get that it's hard. But these videos don't seem all that different from what a good tutor would do, as you point out -- except without the interactivity, which is a big part of what a good tutor does. And the videos could use some editing; they feel like rough cuts of something better.posted by madcaptenor at 10:17 AM on May 28, 2011

@madcaptenor: Also, a common criticism of the Khan Academy videos -- and one that I share from what little bit of them I've seen -- is that even though they're free, they belong to what you might call the tutoring-industrial complex.

That doesn't seem like a criticism as much as a correct interpretation of his focus. The criticism, I assume, is that the tutor-complex needs fixing and he should be fixing it instead of merely putting his finger in the dyke. As you say, he isn't revolutionary enough. Fair enough.

But the thing I like about Khan Academy is that it gives large payoffs for curiosity. People long out of college and far removed from any hoops have talked about the joy of discovering math through his system. His series on the credit crisis, for example is strictly for awareness, not an exam or curriculum. That seems like a purer form of learning than being a part of a complex.posted by acheekymonkey at 10:21 AM on May 28, 2011 [2 favorites]

This past Fall, I started a Khan academy-based "math club" at my kids' K-8 school, in which kids mostly did the nicely designed Javascript exercises, but also watched the videos, and interacted with each other and the adults in the room when they had questions. It was a success, in that parents (and kids) reported looking forward to doing math, which replaced an almost universal dread.

Next year I'm planning on returning to a more open-ended "math circle" format (with a Khan academy option). I believe that having a math club available at the school, even though it's only once a week, has shifted the "hallway attitudes" towards math. It's been gratifying, and I recommend it to any parent with a couple hours free per week (and an available computer lab after school).posted by dylanjames at 10:28 AM on May 28, 2011 [6 favorites]

I didn't mean that any of those described you, or anybody else that's reading this. But these are flaws that are common to a lot of people.

I'm not taking it personally. But, one of the biggest problems in university education in the US is the persistent idea that learning is something a teacher does to a student: student pays a fee to go into a room with teacher/tutor, t/t does something, student leaves the room with knowledge. The hard fact of learning is that it's 90% you and sitting in a classroom is a small fraction of the process. A bad teacher can get in the way of you learning, but you yourself are by far your biggest obstacle. I think that US culture has a very Roman attitude towards education which it inherited from merry-old-England: learning is a luxury imported from abroad, a kind of expensive decoration. And it shows, even at podunk community colleges.

And this is enough? Not being terrible? I guess it's a start.

but a start of what? computerized learning (IMHO) is driven cost-saving at large public universities where quantity is more important than quality. The major weakness of it all is *computerized assesment* which restricts problems to ones that are either multiple choice or numerical answer. the end result is very much driven by the assumption that public university students won't largely amount to more than drones whose purpose to is follow simple instructions in an office setting.

you could do a lot more with dealing with the wide disparity of skills of students coming into a public school environment using computers but most projects, to me, seem to be about mechanizing an already not so great educational experience.posted by ennui.bz at 10:40 AM on May 28, 2011 [8 favorites]

The criticism, I assume, is that the tutor-complex needs fixing and he should be fixing it instead of merely putting his finger in the dyke. As you say, he isn't revolutionary enough. Fair enough.

I'm not sure I follow the point about the tutor complex and Sal's responsibility to it. Math education is deeply flawed, but only because it's been hijacked and abused as a learning talent filter for the military-industrial-education-complex, and so it becomes mandatory on a warehouse schedule, deliberately moving unprepared kids forward using a lecture learning model that doesn't stop for anyone. And this has everything to do with cultural educational priorities. The result is that about 80% of all students learn to fear and therefore hate all math.posted by Brian B. at 10:41 AM on May 28, 2011 [5 favorites]

And the videos could use some editing; they feel like rough cuts of something better.

I like that he sometimes stammers a bit and makes mistakes, tbh. His personality really shines through in the videos and makes it feel like a regular guy can do this stuff without being a super genius (though he may be a super genius)posted by empath at 10:42 AM on May 28, 2011 [2 favorites]

And, btw, for those saying 'this is just what a good tutor does' -- do you not realize how revolutionary it is to have a 'good tutor' available for everyone for free?posted by empath at 10:44 AM on May 28, 2011 [28 favorites]

I'm thrilled with this. I hate that I was never much good with math and I especially hated that how it was taught meant that I couldn't go back and figure out stuff for myself (I am rather an autodidact and learn best if I can figure it out on my own with good sources.)posted by St. Alia of the Bunnies at 10:46 AM on May 28, 2011 [2 favorites]

I like that he sometimes stammers a bit and makes mistakes, tbh.

Agreed. He messes up with the color selection, he goes back and rewrites stuff, it's good.posted by kenko at 10:47 AM on May 28, 2011

I like that he sometimes stammers a bit and makes mistakes, tbh.

Funny. As a university instructor, I make one mistake on the board that requires my room of 50 scribes to erase something, and there is nearly widespread mutiny followed by 10 minutes of "tuning out" because "the teacher doesn't know what he's talking about".

Sigh.

I haven't watched a lot of his videos. I just watched the one for the chain rule. It was terrible. Like madcaptenor says, it's not a lecture on the chain rule, or why it works the way it does. He's even presenting the idea backwards; I think it is much more helpful to think of differentiation as working from the "outside in" not the "inside out" like he does.

I'm with ennui.bz. Students don't understand that it is 90% their effort. So, the thing is when they go, of their own volition, to the Khan Academy site and watch videos and learn something, they feel good. This is because they finally learned how to take derivatives, or add fractions, or whatever. Then, when they come to my class, they sit there passively, copy things down furiously without paying attention to what they're writing, then go home and to think I'm a "terrible teacher", and sit down at the Khan Academy page and actually learn something.

Actually, I'm fine with them thinking I suck if it gets them to learn something.posted by King Bee at 10:51 AM on May 28, 2011 [4 favorites]

room of 50 scribes

There's the problem.

I'm not saying I know what the solution is. But we have textbooks! Why are they writing down everything we say?posted by madcaptenor at 10:57 AM on May 28, 2011

Why are they writing down everything we say?

I don't know. Some teacher somewhere told them that that's what you need to do to be a good student. Sometimes, I'll take class periods where I write nothing down for an extended length of time. They really start getting uneasy.posted by King Bee at 10:59 AM on May 28, 2011 [1 favorite]

I haven't watched a lot of his videos. I just watched the one for the chain rule. It was terrible.

No, it's not terrible. Terrible is a talking paper-clip or pages of gibberish in a mauve font or random crashing java applets in between incoherent textbookese.

I'm with ennui.bz. Students don't understand that it is 90% their effort.

I don't want to be too anti-student. Teaching at large public universities in the US is often legitimately terrible, but the reasons have little to do with classroom/lecture teaching.

I'm not saying I know what the solution is. But we have textbooks! Why are they writing down everything we say?

Because you learn in high school that math is the class where the teacher tells you how to do something meaningless but simple, and then asks you to parrot it back on a test. Copying it down is the first step, and everything is more efficient if the teacher is a computer program. The thing is that this approach works very well in Taiwan (and I guess the PRC too) it's just that American students can only parrot very simple things, with a high error rate. Parroting complicated tasks actually takes a functioning educational system. NOT-PARROTISTposted by ennui.bz at 11:01 AM on May 28, 2011 [2 favorites]

Saying that the burden of learning something is on the students (which is true) is not anti-student. It is as pro-student as you can be. Bad teachers will say things like "but I taught you how to do this, you should know it already". Bad teachers think much of the burden is on themselves, and as long as they are "good", then the students can go screw themselves.

Because you learn in high school that math is the class where the teacher tells you how to do something meaningless but simple, and then asks you to parrot it back on a test.

This is what needs to change. We can start by not having people who "love to work with children" but hate mathematics in all of its forms instill that same hatred in those children.

Everyone knows that something is wrong. The politicians say, “we need higher standards.” The schools say, “we need more money and equipment.” Educators say one thing, and teachers say another. They are all wrong. The only people who understand what is going on are the ones most often blamed and least often heard: the students. They say, “math class is stupid and boring,” and they are right.

"Because it's a nonprofit, it's able to attract all kinds of talented dreamers, many of whom work for free..."

Thanks for bringing the double entendre inherent in "class war" so firmly into view.

I'm a university professor who teaches math and physics to engineering students, so you can skip what I have to say as just hypersensitivity or resentment, if you like. But, truth be told, I am all for these videos, in themselves. I like the internet, self help, and believe in life long learning, so really, what's not to like?

Well, what's not to like is not the videos themselves, but the implications being drawn from them and the social agendas that I just know are coming down the track right along side them. And it matters not whether Khan has these agendas himself. When I listen to how this guy is being lionized, I can feel the bile rising. I do not think it is possible to honestly or accurately examine the Khan Academy outside of the context of the current ferocious revival of know-nothingism, the current attacks on public education, and the general climate of corporate capture of civic functions. So, yeah, I have a number of issues with this stuff.

In fact this thread is illustrating one of my issues very nicely: we're seeing repeated here the oft-heard claim that our education system is terrible--but really this is just a received notion. It is the apple pie and motherhood of man-in-the-street social criticism. It is a something we think makes sense, since few of us loved school. But as adults we fail to separate out the realities of our psycho-social development back then with our assessment of the teachers. I mean, do adolescents like anything? Do you not see the difference between looking at these videos as a self-motivated adult and being forced to look at them for class at the age of 13? Do you not realize how infinitely ignorable a video is?!

We also can easily believe our education sucks because we look at our world. My anarcho-lefty eyes see it in the fact that Bush the plutocratic idiot got elected two times, Palin and Bachmann are popular, more people believe in the Left Behind series than in basic scientific facts, the human race seems to be incapable of responding constructively to a swarm of global disasters of our own making... But is this the result of bad schools? People are stupid and ignorant. This does not imply that schools are bad. The schools are embedded in a social matrix, and in the US this matrix is relentlessly anti-intellectual. Is it fair to expect schools to be able to overcome the Idiocracy that is being carefully crafted using billions of dollars of resources and pumped out relentlessly via hundreds of communication channels, 24/7?

None of the stuff in these videos is different from what every good teacher already does: set up problems with intuition; use concept mapping; motivate with examples; perform examples with a running commentary on concepts, methods, and pitfalls.

I haven't looked at many of these videos. The ones I've seen seem pretty good. Nothing earth-shattering. Just good. I'm glad that many math phobes have found them helpful. I'll certainly be recommending them to students as an option. So, sure, by all means let's enjoy using them. But let's not use them to make sweeping judgments about our education system. And, above all, let's understand how they might be used illegitimately by the anti-public-education, for-profit school assholes.posted by mondo dentro at 11:10 AM on May 28, 2011 [35 favorites]

Well, what's not to like is not the videos themselves, but the implications being drawn from them and the social agendas that I just know are coming down the track right along side them. And it matters not whether Khan has these agendas himself. When I listen to how this guy is being lionized, I can feel the bile rising. I do not think it is possible to honestly or accurately examine the Khan Academy outside of the context of the current ferocious revival of know-nothingism, the current attacks on public education, and the general climate of corporate capture of civic functions. So, yeah, I have a number of issues with this stuff.

yup. in a nutshell. The Gates foundation does not have the best interests of lower-class students at heart.

In fact this thread is illustrating one of my issues very nicely: we're seeing repeated here the oft-heard claim that our education system is terrible--but really this is just a received notion.

But the system I saw my students in (teaching math to engineers and sundry at a large public university) was terrible and it's a circular problem because the biggest issue is the culture of the students coming in (followed by neglect by the people who should have been responsible.) I felt responsible but in reality could do little.posted by ennui.bz at 11:18 AM on May 28, 2011 [3 favorites]

I felt responsible but in reality could do little.

I feel much the same way. By the time we get the students they've been through over a decade of schooling; since we live in reality, not Dead Poets Society, one class isn't going to change anything.posted by madcaptenor at 11:27 AM on May 28, 2011 [1 favorite]

In fact this thread is illustrating one of my issues very nicely: we're seeing repeated here the oft-heard claim that our education system is terrible--but really this is just a received notion.

Received from whom? I went to public school, I got to experience how much it sucked directly.posted by empath at 11:34 AM on May 28, 2011

mondo dentro:
I spent a year in a math program in Hungary in 2002, and one of the really striking things was that when talking to Joe Anybody, they generally had fond memories of doing math in school. There is something uniquely American in the problems in American math education, and I personally think it has a lot to do with the industrial model of education. Math curricula as they stand today were established in the 1940's to produce mass quantities of engineers who could do rote computations ad nauseum. And they're simply irrelevant today.

I personally think there needs to be a more problem-solving oriented approach to math teaching in place. Most courses now are 'techniques' courses, where particular aspects of math are treated in detail, giving the students very particular tools. These classes are indeed boring and stupid if you're not already convinced that you need these skills. And this is where problem-oriented classes come in: the idea is to learn tools for attacking problems mathematically without having a lot of background knowledge in place. Students get practice very relevant to the world outside the classroom, and simultaneously get introductions to techniques that warrant taking whole other classes to master (such as linear algebra).

I'm very interested in hybrid teaching models, using a mix of electronic resources and human resources. There are definitely strengths to the electronic medium, and they aren't mutually exclusive from the strengths of a human teacher. Mixing the two you get something better than either.

As an example, I helped design a linear algebra course a couple years ago that used online homework for drill-type exercises, but also had significant written homework as well. The drills were instantly graded by the machine, giving instant feedback a hundred times better than students ever get on written drill homework, and also chances to correct (and learn from) their mistakes. Meanwhile, the written problems focused on conceptual and problem-oriented thinking, the kinds of things that machines can't grade. The approach was quite successful, I think.posted by kaibutsu at 11:36 AM on May 28, 2011 [4 favorites]

I went to public school, I got to experience how much it sucked directly.

I mean, I learned trig from a gym teacher who hated math and called me a nerd for giving a shit.posted by empath at 11:36 AM on May 28, 2011 [5 favorites]

But we have textbooks! Why are they writing down everything we say?

Different students have different learning styles. I'm one of those who does learns very well from a lecture when I'm paying attention and taking down notes. If I take the trouble to organize the notes as I'm writing them down, the structure often helps me to understand things right then and there. On the other hand, I find reading textbooks extremely boring, and tend to use them only to fill in the gaps from things I didn't get in lecture. So if you'd had me in your class, you'd probably have noticed me scribbling something away furiously, but that really doesn't mean I wasn't understanding what you were saying or that I was just blindly copying down things.posted by peacheater at 11:38 AM on May 28, 2011 [6 favorites]

I mean, I learned trig from a gym teacher who hated math and called me a nerd for giving a shit.

Received from whom? I went to public school, I got to experience how much it sucked directly.

Yeah... And so this personal experience directly implies that our educational system is bad.

Hey! I know! We can take this poorly drawn conclusion as further evidence that our educational system is broken! It's a perpetual motion machine of suck!posted by mondo dentro at 11:40 AM on May 28, 2011 [2 favorites]

Different students have different learning styles.

Alright, to be honest, I was always one of the people who wrote down everything in lecture. (Or at least tried to.) The funny thing is that I very rarely looked at my notes after I wrote them - something about the act of writing forced me to focus.

It still freaks me out when I have a room full of students who would write down every damn thing I say, though. I mean, what if I'm wrong?posted by madcaptenor at 11:41 AM on May 28, 2011

These classes are indeed boring and stupid if you're not already convinced that you need these skills.

Why is it that mathematics is a subject which constantly has to legitimize its existence? I don't often hear students complain "why do I need to learn grammar" or "why are we reading Shakespeare" or "who cares what electrons are". They just accept that in a grammar, literature, or physics class, this is the thing that you do.

In math classes, it's always "what is this used for". Often, the answer is nothing. They don't like that, because they were raised to believe that "math is the language of the universe" (whatever that means) and that math is all around you, and that math is the mystery language that scientists use to talk to each other. None of those things is true.

Different students have different learning styles.

I understand that. I don't know what kind of attention span you have, but it is quite difficult to understand what I'm saying while writing down something else that was written on the board. Hell, it's hard to even hear what I'm saying when you're focused on writing down another sentence which I'm not speaking. In fact, it wasn't until my third year of graduate school that I just stopped taking notes and actually started paying attention to the lecture, I mean really paying attention. I learned a lot more that way.posted by King Bee at 11:45 AM on May 28, 2011

I never took notes. How can you pay attention when you're scribbling stuff on paper?posted by ryanrs at 11:46 AM on May 28, 2011 [1 favorite]

I don't often hear students complain "why do I need to learn grammar" or "why are we reading Shakespeare" or "who cares what electrons are". They just accept that in a grammar, literature, or physics class, this is the thing that you do.

You don't hear them complaining about those things because you don't teach those subjects.posted by madcaptenor at 11:48 AM on May 28, 2011 [9 favorites]

it is quite difficult to understand what I'm saying while writing down something else that was written on the board.

How can you pay attention when you're scribbling stuff on paper?
Apparently I have some mad skillz that some of you don't have, but I've never found this very difficult. YMMV.posted by peacheater at 11:49 AM on May 28, 2011 [3 favorites]

In math classes, it's always "what is this used for". Often, the answer is nothing.

The answer is almost never nothing, especially for high school math. It's just that it seems like the teachers in High School don't know or don't feel like answering it.posted by empath at 11:49 AM on May 28, 2011

Some of us learn much more effectively by taking notes in a lecture, which is why we take them. Reading the textbook, especially in math (not my strong suit), just doesn't work well for me. I'm not a robot doing that because that's what I was told to do. It's how I learn best.posted by rtha at 11:50 AM on May 28, 2011 [1 favorite]

"what is this used for". Often, the answer is nothing.

Huh? Any basic engineering uses pretty much everything up through differential equations, at least. High school students don't know what they're going to do as a career.posted by ryanrs at 11:50 AM on May 28, 2011

In math classes, it's always "what is this used for". Often, the answer is nothing. They don't like that, because they were raised to believe that "math is the language of the universe" (whatever that means) and that math is all around you, and that math is the mystery language that scientists use to talk to each other. None of those things is true.

Anyway, I do agree with this part though. I find this constant need to justify math with "real-world applications" extremely frustrating. On preview, yes often there are real-world applications later down the line, but in the beginning it helps to think of math as just a new way of looking at things, like learning a language. There is a lot of beauty in abstraction that I feel that this whole approach completely misses out on.posted by peacheater at 11:52 AM on May 28, 2011 [1 favorite]

The drills were instantly graded by the machine, giving instant feedback a hundred times better than students ever get on written drill homework. Meanwhile, the written problems focused on conceptual and problem-oriented thinking, the kinds of things that machines can't grade. The approach was quite successful, I think.

Bravo. It's sounds like a good system. But surely this sort of thing is not really new, is it? It seems to be ubiquitous on university campuses, that's for sure.

When you say "problem solving approach", aren't you just talking about word problems? And, when you say "100 times better" and that the approach was "quite successful", this was assessed how?

But, let's be clear: my gripe is not about innovation or having online videos. It's about the fact that a rich outsider hobbyist comes along doing things that many, many, MANY, educators already do, and somehow he's some sort of great education innovator. He's not.posted by mondo dentro at 11:53 AM on May 28, 2011 [1 favorite]

It's about the fact that a rich outsider hobbyist comes along doing things that many, many, MANY, educators already do, and somehow he's some sort of great education innovator.

If they were doing it, they'd have 100,000 hits on youtube, too. He didn't use his connections or his wealth to get popular. He was popular well before anybody gave him a dime, and well before he had connections. Because what he was doing worked.

in the beginning often there are real-world applications later down the line, but in the beginning it helps to think of math as just a new way of looking at things, like learning a language

Uh, how did you start learning a language? I started with nouns, not beautiful abstractions.posted by ryanrs at 11:56 AM on May 28, 2011 [1 favorite]

If you think you can do better, do it. No one is stopping you.

I think what stops a lot of academics from doing this is the sense that it wouldn't be rewarded. Sure, you get lots of hits on youtube, but that doesn't count if you're trying to get tenure.posted by madcaptenor at 11:58 AM on May 28, 2011 [1 favorite]

Why is it that mathematics is a subject which constantly has to legitimize its existence? I don't often hear students complain "why do I need to learn grammar" or "why are we reading Shakespeare" or "who cares what electrons are". They just accept that in a grammar, literature, or physics class, this is the thing that you do.

My university is hosting Congress 2011, a gathering of scholars in the humanities and the social sciences. A few hours ago I saw Kwame Anthony Appiah give a talk about 'why are the humanities important?' to a packed auditorium of highly credentialed scholars.

The students might not complain about those subjects*, but someone clearly does.

I doubt it, though. I know I did. Math was obviously useful but at the time I didn't care about "literature".posted by Lemurrhea at 11:58 AM on May 28, 2011

You don't hear them complaining about those things because you don't teach those subjects.

When I took those classes, I never heard those complaints. Of course some people complain about them (people will complain about anything). However, it is not at the frequency with which people complain about math.

Any basic engineering uses pretty much everything up through differential equations, at least.

At no point will you encounter a solid object which is actually the region in the first quadrant bound by the x-axis, the line x=1, and the curve sqrt(x) revolved around the x-axis. Neither will you be concerned with the volume of such an object, because you will never encounter it. Nevertheless, this is one of the things we study in calculus.posted by King Bee at 12:03 PM on May 28, 2011 [1 favorite]

QFT: "And, btw, for those saying 'this is just what a good tutor does' -- do you not realize how revolutionary it is to have a 'good tutor' available for everyone for free?" - empath

Oh, so YouTube is now that bar educators are supposed to jump over? Have you so thoroughly imbibed of consumer culture that you equate mass popularity with quality? Do you think that the MacDonalds "billions sold" statistic makes them excellent chefs, even of burgers?

If you think you can do better, do it. No one is stopping you.

I am doing what I think I can do better. Thanks for the permission.

Seriously, I don't mind if you didn't read what I wrote (boring, TL;DR and all that), but you're arguing the totally wrong topic if you think I have a problem with having popular teaching videos online.posted by mondo dentro at 12:08 PM on May 28, 2011

Uh, how did you start learning a language? I started with nouns, not beautiful abstractions.
Well, yes, that's pretty much what I'm trying to get at. In a sense, abstractions are the nouns of mathematics, they're the bread-and-butter of mathematics. Think about algebra. Before you can solve complicated word problems in algebra, you need to understand that x represents an unknown quantity, that this equation tells you something about x, but in an indirect form, that we can manipulate the equation to get the information about x in a more direct form. This is a pretty complicated concept to grasp, if you think about it, and it's perhaps the first encounter most children have with abstraction in school. Yet before they've even grasped this completely, understood all the manipulations they can do, and done many many problems so that they truly understand what's going on, teachers expect them to apply this rather nebulous concept to "real-world examples." I would argue that that's expecting children to write poetry before they've acquired much of any vocabulary.posted by peacheater at 12:10 PM on May 28, 2011 [1 favorite]

@ryanrsHuh? Any basic engineering uses pretty much everything up through differential equations, at least. High school students don't know what they're going to do as a career.

Very few people actually become engineers, and very few engineers actually use anything except the LAST few years of their math training. The rest is done by computer. When was the last time you actually multiplied two large numbers by hand, or divided two fractions? Is drilling young children on these algorithms five days a week for 2-6 years actually helping them become better engineers? Or does it make more sense to teach students to understand multiplication as proportionality, rate, dilation, and rotation, so that they know WHEN to use it, and let the computer do the algorithmic work, like engineers actually do? Is the best answer to do some of both?

These are genuine questions. Everyone has an opinion, but real research on these topics is sketchy to non existent. Attempts to study them meet a lot of resistance from parents, teachers, and professors, because the purpose of a mathematics education is not to become a good engineer. It's to prepare students for the next math class, or to pass a standardized test. The test doesn't check if you have a good image of multiplication suitable for engineering, it checks if you can multiply two large numbers by hand. When you do research on students, you're playing with those student's future careers. You have a responsibility to make sure those students pass their tests, pass their class, are prepared for the next class, get into a good school, etc. It makes questions like the above VERY difficult to answer empirically.posted by yeolcoatl at 12:11 PM on May 28, 2011 [1 favorite]

At no point will you encounter a solid object which is actually the region in the first quadrant bound by the x-axis, the line x=1, and the curve sqrt(x) revolved around the x-axis. Neither will you be concerned with the volume of such an object, because you will never encounter it. Nevertheless, this is one of the things we study in calculus.

Knowing how to find the volumes and areas under curves comes up all the time in real life. Probably not while working at McDonalds, but there are tons of real world applications for it.posted by empath at 12:12 PM on May 28, 2011

Very few people actually become engineers, and very few engineers actually use anything except the LAST few years of their math training.

That's why I think that very few people should be learning calculus, unless they're genuinely interested in it, and we should not be forcing it down people's throats. But if people are interested in learning it, it should be made as easy and cheap as possible to do so. Personally, I don't see any benefit whatsoever in going to school to learn this stuff, if these videos (and others like them) explain the concepts well enough (and I think they do).posted by empath at 12:16 PM on May 28, 2011

And really, how often in real life do you need to know the ratio of a the side of a right triangle adjacent to an angle to the hypotenuse? Trigonometry, in high school, seemed like the most worthless, abstract nonsense to me.

If someone had explained to me how sine and cosine relate to pi and the exponential function, and how they all related to harmonic functions and quantum mechanics and sound and music and a million other concepts, I would have been all over it. But it was always presented to us as "you need to know this to pass the test, and you need to pass the test so you can get to college."

Math was never presented to us as something that should be interesting for its own sake. And I was in honors and AP classes. I can't imagine how much worse it was for people in A levels.

The question: "What do I need to know this for?" isn't always asking about "How can I use this in real life, for some practical purpose?" -- it's about "How can knowing about this enrich my understanding of the world?"posted by empath at 12:24 PM on May 28, 2011 [5 favorites]

As an aside, can we lay off on disparaging note-takers? I take copious notes in class, and yes, I'm listening, engaged, and paying attention. It's just the way I learn best. I have a fantastic memory for stuff I've written down (near-photographic), and once I've written something down, I remember things about a million times better than when I just hear it. The stuff I'm writing down isn't just a transcription of the lecture material, either; I process and structure the information, note questions about the material that I'd like to look up later, connections with other material, why a piece of information is important, etc. It's just how my brain works.

Honestly, some people do take terrible notes, and I have no problem believing that their performance improves when they stop writing down random crap or simple transcription (I have a friend who mostly takes notes about how tired she is in class...). But some people take great notes, and that process noticeably improves their learning outcomes. Please don't reflexively judge them as "not paying attention" or unthinking "scribes" or whatever. Thanks.

Back on topic, I think that the main culprits in the "why do I have to learn this?" chorus (at least at the college level) are definitely the engineers. There was almost a knock-down, drag-out fight in my calculus class over why the engineers even had to learn to do derivatives by hand, since they'd just use calculators to do it later anyway. Sigh. To his credit, my instructor gave a lovely speech about the beauty of math and made them do it anyway.posted by dialetheia at 12:36 PM on May 28, 2011 [2 favorites]

Neither will you be concerned with the volume of such an object, because you will never encounter it.

Sounds like an ogive. Square root isn't a commonly used curve, but the shape is commonplace.

Very few people actually become engineers

Very few people doctors or teachers or construction workers. Very few people go into any one specific field.

very few engineers actually use anything except the LAST few years of their math training. The rest is done by computer. When was the last time you actually multiplied two large numbers by hand, or divided two fractions?

Every single day. Are you seriously suggesting that engineers don't need to know basic arithmetic? Sure, I don't multiply six digit numbers by hand with paper and pencil. I do it in my head and only carry the calculation to two significant figures. But I do it constantly, which is why I'm so good at noticing typos in technical data and documentation. The only time I use a computer for arithmetic is when I'm dealing with many values and need to give them names. I don't own a calculator.posted by ryanrs at 12:36 PM on May 28, 2011 [2 favorites]

As an aside, can we lay off on disparaging note-takers?

Okay. I think that some people are disparaging note-takers because they sense that some of the students really would learn better if they weren't taking such detailed notes but they do it anyway. And ranting about this on the Internet is easier than actually identifying those students and saying to them "you know, maybe you'd do better if you didn't worry so much about writing everything down". I'm sure some of my students should be taking less notes but I don't know who they are, and I'm not sure it's my place to tell them how to learn anyway. iIknow what works for me but that doesn't mean I know what works for them.

The stuff I'm writing down isn't just a transcription of the lecture material

The stuff a lot of my students are writing down is just a transcription of the lecture material. And not a good one at that. as I learn when they show me their notes and ask "what did you mean here?" and they show me something that I'm pretty sure is not what I said.posted by madcaptenor at 12:42 PM on May 28, 2011 [1 favorite]

Sounds like an ogive. Square root isn't a commonly used curve, but the shape is commonplace.

We're talking about two different things. The things in that wikipedia article are made of matter, and hence, atoms. So, those curves are not smooth curves like the curve I have in my imagination. So, no, even though the article says "The traditional or secant ogive is a surface of revolution of the same curve that forms a Gothic arch", that's just wrong.

The stuff a lot of my students are writing down is just a transcription of the lecture material. And not a good one at that. as I learn when they show me their notes and ask "what did you mean here?" and they show me something that I'm pretty sure is not what I said.

I have had this same experience multiple times.posted by King Bee at 12:48 PM on May 28, 2011

this is where i think khan is 'taking it to the next level' (as he explains in the video ;) rather than a forced march, it's the learning modules, exercise platform and other tools for teachers he's building (with teacher input) at khan academy -- perhaps moreso than the videos themselves -- that allows a transformation of 'the industrial model of education' by using technology to 'humanize the classroom', which dareisay, is exciting and, yes, perhaps even revolutionary... from the BW article:

Used in the classroom, the Khan Academy flips the traditional curriculum; students listen to the lectures at home, on their own time, and do the homework in class, which allows the teacher time to address student issues individually. As the class progresses, Julian wanders through the desks with an iPad running Khan's dashboard, so he can see who's ahead and who's behind. He doesn't really need it: He already knows exactly how each student is progressing. And he isn't doing as much individual teaching as one might expect. Often, the lagging students are tutored by the students who are ahead. "The kids know whom to call on," says Julian. "It happened on its own. They just began to get out of their seats and work with each other. They've identified their trustworthy peer tutors. They know they can call on Sriram and Akhil and Albert, and that they know what they're talking about. Mainly, I've had to spend time teaching them how to teach."

Erin Green, principal of Covington, loves the Khan Academy and plans to expand it to more classrooms. "Many of the students are working at a level of mathematics that I have never seen in an elementary school before, maybe not even in a junior high school before," she says. "They're engaged and they're excited, and that's the most exciting part. It meets you at your level."

The Khan Academy has also been introduced in two seventh-grade classrooms for struggling learners in the Los Altos district, and the district is considering using it in all schools next year. "Their improvement has been dramatic," says Khan of the slow group, who notes that his studies are small, not peer-reviewed, and just intended for him to get a sense of whether Khan Academy methods are working or not.

The things in that wikipedia article are made of matter, and hence, atoms. So, those curves are not smooth curves like the curve I have in my imagination.

So what you're saying is that volume integrals are useless because of the quantization of matter? How am I supposed to take this argument seriously?posted by ryanrs at 1:04 PM on May 28, 2011 [2 favorites]

Buried in on of the many links at the top is his TED talk. In it he really hits on the advantages of video learning.

Lecture/Homework model:

Someone talks at the front of a room for an hour while you sit suffering with allergies barely able to see the blackboard much less concentrate on anything. Homework is assigned which you attempt to complete but have no idea if you're doing it correctly or not. Lecture moves on to the next topic building on the previous topic, but you didn't quite understand that and now it's just a frustrating exercise in being left behind. Your homework is returned several days later with half your problems marked incorrect, but you don't know why or what you did wrong.

Khan Academy model:

Watch a video explaining a concept. Pause it, sneeze, clear your head. Continue, didn't quite get something? Rewind it, replay it. Get it. Do the exercises online. Make a mistake, get instant feedback about what you did wrong and how to complete it correctly. Move on do more problems, make more mistakes but getting instant feedback about where your errors were and how to correct them. Complete 10 questions in a row without errors, get a gold star, move on to the next video.

The fascinating thing is that the imaginary object I have in my mind has anything to do with the physical Gothic arch. They are not the same thing. The fact that the one can be used to say anything about the other is what is cool, not that the arch is an actual instance of this imaginary thing (because it isn't).posted by King Bee at 1:06 PM on May 28, 2011

We're talking about two different things. The things in that wikipedia article are made of matter, and hence, atoms. So, those curves are not smooth curves like the curve I have in my imagination.

My living room is made of matter, and hence atoms, and is not actually a perfect square of 11 units on the x axis and 13 on the y axis. Nevertheless, that abstraction does usefully approximate the situation, and allows me to determine that my living room is about 143 square feet, and that lets me buy air conditioners and carpets and furniture. Math becomes 'useful' when we use it to approximate real-world objects and movements and interactions.

Some situations require closer approximations than others, but at the end of the day, NASA shot a bunch of guys onto the moon on a regular basis by using math to approximate the real, physical, atoms-and-matter thrust of a rocket with some guys balanced on top.posted by Tomorrowful at 1:09 PM on May 28, 2011 [3 favorites]

(in my previous comment please substitute "rectangle" for "square;" in an earlier draft of the comment I referred to my bedroom rather than my living room. I will now commit seppuku.)posted by Tomorrowful at 1:10 PM on May 28, 2011 [1 favorite]

Do you similarly argue against teaching Newtonian physics? That doesn't hold up at the quantum level either.

You have the perspective of a person who has never actually used math to build stuff.posted by ryanrs at 1:10 PM on May 28, 2011 [2 favorites]

Some situations require closer approximations than others

When purchasing electronic components, accuracy to two significant figures is standard, three costs extra, and four is a special order. Electrical engineers do not count electrons.posted by ryanrs at 1:13 PM on May 28, 2011 [1 favorite]

You have the perspective of a person who has never actually used math to build stuff.

That's because I'm a mathematician.

I'm not arguing against teaching anything. I'm arguing against people giving "real world" examples of things which are completely imaginary. It mucks everything up, and sends the wrong impression. I'm not talking about a specific Gothic arch, I'm talking about this imaginary thing which happens to resemble this Gothic arch, but is far more perfect than this Gothic arch could ever hope to be.

Mathematics is the most beautiful thing mankind has ever conceived of, in my opinion. That alone should warrant its study.posted by King Bee at 1:16 PM on May 28, 2011 [3 favorites]

You original statement was: In math classes, it's always "what is this used for". Often, the answer is nothing.

My position is that that is a lie. Volume integrals are sometimes used in engineering. Just about everything in high school math is used in engineering. To say it has no purpose is to deliberately mislead your students.posted by ryanrs at 1:23 PM on May 28, 2011 [1 favorite]

Let me put it another way. I use high school math and physics to inform my understanding of the world around me. I do not use numerical analysis and quantum mechanics because they are really quite poor tools for that job.posted by ryanrs at 1:27 PM on May 28, 2011 [1 favorite]

At no point will you encounter a solid object which is actually the region in the first quadrant bound by the x-axis, the line x=1, and the curve sqrt(x) revolved around the x-axis. Neither will you be concerned with the volume of such an object, because you will never encounter it. Nevertheless, this is one of the things we study in calculus.

I have no idea what you are arguing... the point of this exercise is that it is an exercise. It's like you are learning to playing the piano and complaining "when am I every going to perform a scale." There are vanishingly few functions which are integrable in the intro. calculus sense of the word... that's a theorem. So, any exercise you can do without recourse to numerical approximation is a good thing to learn to do when you are learning about multiple integrals (especially functions of multiple variables.) Whether performing said integral(s) under time pressure is a good basis for letting you into med school or letting you program social apps for web 3.0, I'm not so sure about, but pedagogically it's something you might as well do in a calculus class.

Watch a video explaining a concept. Pause it, sneeze, clear your head. Continue, didn't quite get something? Rewind it, replay it. Get it. Do the exercises online. Make a mistake, get instant feedback about what you did wrong and how to complete it correctly. Move on do more problems, make more mistakes but getting instant feedback about where your errors were and how to correct them. Complete 10 questions in a row without errors, get a gold star, move on to the next video.

Library card: Free
Access to Khan Academy: Priceless

This is so glib; but you'll go far if you can spout this kind of crap and believe it. It's like you've scripted out a commercial for a product you are selling. My son and I make fun of the ten problem gold star thing; it's a kind of one size fits all approach that is reasonable for a computer but would be laughable in real life with a real teacher. You are fetishizing a limitation of the software.posted by ennui.bz at 1:29 PM on May 28, 2011 [1 favorite]

I'm not arguing against teaching anything. I'm arguing against people giving "real world" examples of things which are completely imaginary. It mucks everything up, and sends the wrong impression.

oh i get it. I actually agree. sorry.posted by ennui.bz at 1:31 PM on May 28, 2011

Clarification: the original question asked for real world examples of uses of math, not examples of objects described by any particular word problem. I.e. "when will I (student) ever use this (math)."posted by ryanrs at 1:37 PM on May 28, 2011 [1 favorite]

You can consider this anecdata, but speaking as one who most people would consider having a strong facility with math (I have a physical science bachelor's degree which was very math-heavy), I consider math by far my weakest area -- I got by more on being able to grasp the concepts, physically, of what was happening (which is why I struggled so much in Quantum Mechanics where physical intuition will only get you so far) than by being able to throw the numbers around.

I believe the reason for this is that, despite me being aware from the very beginning that math was the key to science and being fairly motivated to learn, I had with VERY few exceptions, math teachers in elementary school, high school, and college who fell into one of two camps:

Among elementary school teachers, they hated math, and couldn't hack it. Pre-algebra was a stretch for them and they had no sense of how any of it "worked." Explanations that led to intuitive understanding were virtually nonexistent.

Among my high school teachers, I had one very good teacher who had a gift for explaining what was really going on. Trig/Pre-Calc The only math class in HS that I aced handily, after BARELY passing Algebra II. In High school, if you aced the tests but didn't do all the homework, you were penalized. It became an authority game of submission rather than the goal being understanding. I got a D in algebra II because of that.

Among my college math professors, I could tell they knew their shit. The sad thing is some of them probably didn't want to be babysitting undergrads 3 hours a week in lectures, so the classes I did well in were the ones excited about teaching (Calc 1st year), and the ones I didn't do so well in were the ones who just flew on their notes (I had a good TA that helped me "get" triple integrals).

Something like the Khan Academy might have made the difference between me graduating with a respectable GPA but not bound for grad school to maybe making it out with honors and moving on to a Ph. D.posted by chimaera at 1:43 PM on May 28, 2011 [3 favorites]

yup. in a nutshell. The Gates foundation does not have the best interests of lower-class students at heart.

Oh, they have them at heart. The ultimate consequence of what they want to do may not be good for them, but if they didn't genuinely care, why would they do it? The problem is that like many ultra-achieving technocrats, Bill Gates has trouble imagining what it would be like to be other than he is. As a result he wants to build a school system that would be perfect for a 6-year old Bill Gates.

Also, why do people keep bringing up universities and colleges? I don't see anything beyond high school math among those lessons, with the exception of some of the more advanced linear algebra and differential equations material and even those are first year courses at university.

The short video + practice questions approach would seem to be pretty well suited for basic math like this. Especially when you pair it (as Khan suggests) with a teacher whose role is to help students understand problems rather than to lecture to the class.

Obviously no-one does multiple choice or computerised tests at the university level anyway, it simply doesn't work for advanced material because there's so many ways to get it wrong and so many ways that you can misperceive the way to solve the problems. So what, though? That doesn't invalidate the approach for simpler materials.posted by atrazine at 1:57 PM on May 28, 2011 [1 favorite]

I think people bring up college teaching because metafilter has more college teachers than K-12 teachers. Or at least it feels that way to me. More accurately, there are more mefites who teach college and live in my house than mefites who teach K-12 and live in my house. Unless my housemate who teaches high school science is secretly a mefite.posted by madcaptenor at 2:06 PM on May 28, 2011

While I was suffering through the chain rule video, it occurred to me that perhaps the difference people are attributing to the Khan Academy videos is not that students are overcoming bad teaching (I'm yet another person who thinks the idea of pervasive bad math teachers is a received notion), but that students are spending enough time to actually understand the material (or at least enough time to be able to do the problems). There's very little math that requires no practice.

I'm yet another person who teaches college-level math. The idea that there's an increasingly well-known source of math videos appeals to me, but I don't want the tradeoff to be the conclusion that everyone trying to teach math in a formal setting is doing a bad job.posted by hoyland at 2:33 PM on May 28, 2011 [3 favorites]

hoyland: one thing we who teach math in a formal setting may be doing a bad job of is making sure that students know that learning math requires practice.

Or maybe students know this and choose not to practice. (in that case, what can we do to get them to practice? Or should we even bother? Maybe math isn't for everybody and we're just hurting people unnecessarily.)posted by madcaptenor at 2:40 PM on May 28, 2011 [1 favorite]

I am motivated to practice music because when I become better at music, I can play some pretty kickass music.

I think there are bad teachers, but who they are is different for different students. Everyone who fails to learn from a given teacher assumes that teacher is bad; what is likely true is that the teacher didn't present the material in a way that takes with that student.

I believe that people only learn when material is presented in a way that meshes with their prior understanding, so that it fits in, like Lego blocks, with the stuff already known. This is necessarily different for different people, and there is no easy way to know ahead of time what will easily fit. To continue the analogy, sometimes you can "make it fit" with effort and practice, but sometimes no amount of effort will work beyond acquiring the material in a rote, literal kind of way, and sometimes the student himself is unwilling to learn for some reason -- maybe he's told himself the material is too hard and thus can't bring himself to put the effort into learning it, or maybe he has a chip on his shoulder.

The real problem is that teaching effectively is hard, an intractable kind problem that has no definite solution, that always requires wit and insight from a teacher. We have come to take this difficult thing for granted, and because of it education routinely gets short-shrift when it comes to career opportunities and funding.

One thing about Khan I find interesting is that here, unquestionably, the market has failed. Like Craigslist, it is a case where a man cares enough about doing it right to not let petty financial concerns keep him from it.posted by JHarris at 2:48 PM on May 28, 2011 [4 favorites]

Because then you can do some kickass mathematics?

Except, well, it's hard to see why math kicks ass if you don't already know some math.posted by madcaptenor at 2:49 PM on May 28, 2011 [1 favorite]

I am motivated to practice math because.... in order to determine best course of action from a series of acceptable options.posted by Rubbstone at 2:49 PM on May 28, 2011 [2 favorites]

one thing we who teach math in a formal setting may be doing a bad job of is making sure that students know that learning math requires practice.

First, let me lump math and mathematical sciences together (in the physical sciences, a large part of the math learning comes in the science courses).

Given that, I can speak as a "math teacher" and say with great confidence: no way is this true! I repeatedly say this. I repeatedly say "math is not a spectator sport". One of my favorite things to say is "listening to my lectures and thinking you're learning to do this is like me watching you lift weights and thinking I'll get stronger."

I say it. The students get it.... and it seems to not matter all that much.

I believe that the problem is not so much with the teaching, but with the more general system level issue about what we as a society expect education in general to do. Most kids are in school to "get jobs". There is little doubt in my mind that we should have a very high number of our kids getting vocational training--perhaps as high as, say, 80%--rather than being taught in a system designed to produce scholars.posted by mondo dentro at 2:55 PM on May 28, 2011 [3 favorites]

Mondo dentro: I'm sure you say that "math is not a spectator sport" or some variant thereof. I say it too. But just because we say it doesn't mean they get it - just like just because we do some piece of mathematics while they watch doesn't mean they get it.posted by madcaptenor at 2:58 PM on May 28, 2011

One thing about Khan I find interesting is that here, unquestionably, the market has failed. Like Craigslist, it is a case where a man cares enough about doing it right to not let petty financial concerns keep him from it.

This does seem to be the case--but why I and maybe a few others are speaking critically is that the exact wrong conclusion to draw from it is that what's good about what he's doing is somehow a technological innovation. It isn't. I've seen this time and time again in higher ed--the search for a deus ex machina that will make everyone a good teacher.

What Kahn's doing is good because he's a talented teacher. If a shitty teacher does the same thing, it will still suck.posted by mondo dentro at 3:01 PM on May 28, 2011

just because we say it doesn't mean they get it - just like just because we do some piece of mathematics while they watch doesn't mean they get it.

No doubt. But Kahn does nothing to address this aspect of "not getting it", does he? He is using a different delivery system to convey the same content. It will therefore be more easily absorbed by some, and not by others. He happens to be talented, so he might get better results, but if anyone else did it... well, the result would be different.

Putting videos on the internet is not magic. And modularization is as old as the hills. The simple statement that he is "inverting the process" by having the "lectures" at home (i.e. the videos) is really dubious. People used to read at home and come in for class. Now, they can also watch videos. So... we skip the books and just have videos? OK. It's worth a shot. For some things, anyway.

But the bottom line is assessment. Anyone who works in education knows that it's very easy to say something is an awesome new way to learn X. It's another (quite another) to show that it actually makes any difference at all. In this sense, education is way behind the drug industry!posted by mondo dentro at 3:07 PM on May 28, 2011 [1 favorite]

I am motivated to practice math because....

it's a bad syllogism, the moment you start requiring logical consistency from your ideas or designs it's unavoidable... but you can avoid being practiced at it.

Oh, they have them at heart. The ultimate consequence of what they want to do may not be good for them, but if they didn't genuinely care, why would they do it? The problem is that like many ultra-achieving technocrats, Bill Gates has trouble imagining what it would be like to be other than he is. As a result he wants to build a school system that would be perfect for a 6-year old Bill Gates.

Gates isn't a technocrat, he was born rich (from a family of bankers) and by aggressive business practices became a lot richer. His wealth and power come from his success at business, not technology. He's a plutocrat if there ever was one.

His concern is that without technocrats churned out by universities, his business and industry will not be able to continue making huge profits.

One thing about Khan I find interesting is that here, unquestionably, the market has failed.

What a bizarre idea.. the modern educational system has never had anything to do with the "market." The "research university" upon which all of the technology achievements of the 20th century derive was designed by German romantic idealistsposted by ennui.bz at 3:12 PM on May 28, 2011 [1 favorite]

His concern is that without technocrats churned out by universities, his business and industry will not be able to continue making huge profits.

Right on. The essence of modern corporate/financial free market croney capitalism is the externalization of costs to the taxpayer. Public education is good since taxpayers pay to train fodder for industry. Private education is even better, because it adds another layer of profit skimming to the entire enterprise, the tab for which is still picked up by the taxpayers.posted by mondo dentro at 3:21 PM on May 28, 2011

The problem for me is that he didn't have any math that I didn't already know, with the exception of Differential Equations. I watched a few of those and they made them seem really simple (I'd looked at DiffEq before, but not too seriously. There's nothing I really need it for)

I think one problem, or one reason why these are easy to learn is that he's teaching the ideas, while 'real' math classes try to teach you how to apply them over and over again. But with computers and powerful calculators, it's actually just more important that you understand the ideas.

There was another thread about math where someone argued that we need to teach kids math so they learn discipline. That's just insane, it's using math as a punishment to build character and of course making kids hate math in the process!

Anyway, I wish he had more advanced topics like abstract algebra, topology, number theory, that kind of thing.posted by delmoi at 3:30 PM on May 28, 2011

math is all around you, and that math is the mystery language that scientists use to talk to each other. None of those things is true.

Huh? Of course these things are true. Maths is all around you, and won't get anywhere in any sort of science without knowing maths. Maths made the modern world possible.

the question "why are we learning this" should be the easiest thing in the world to answer.posted by moorooka at 5:01 PM on May 28, 2011

Seriously, no, math isn't "all around you". People who allow this idea to persist are doing a great disservice to the field as a whole.posted by King Bee at 5:18 PM on May 28, 2011

People used to read at home and come in for class. Now, they can also watch videos.

Were books free and easily available to anyone at their convenience before?

I think what the people are focusing on the traditional education are missing is that books and classes are inconvenient and expensive. The availability of things like Wikipedia, google books, youtube tutorials and Wolfram Alpha is revolutionary in terms of education. There has literally been nothing like this before in history. It's not that Khan is a brilliant teacher, is that he is the first guy that made the effort to do a brain dump on this scale and with this quality. I wish there were a thousand of him. I wish the people in this thread criticizing him would do it better.posted by empath at 5:31 PM on May 28, 2011 [3 favorites]

Seriously, no, math isn't "all around you". People who allow this idea to persist are doing a great disservice to the field as a whole.

Have you never taken a physics class? The entire universe is nothing BUT math.posted by empath at 5:33 PM on May 28, 2011 [2 favorites]

That apple falling on your head? Maths!posted by moorooka at 5:35 PM on May 28, 2011

If someone had explained to me how sine and cosine relate to pi and the exponential function, and how they all related to harmonic functions and quantum mechanics and sound and music and a million other concepts, I would have been all over it. But it was always presented to us as "you need to know this to pass the test, and you need to pass the test so you can get to college."

If I tried to do this with one of my classes, they would revolt. They're there because the course is required for their major. What they want is to get through it as painlessly as possible. Why they should be required to learn algorithms performed as rituals with minimal understanding to get their degree is something I can't understand, and yet, that's how it is.posted by Obscure Reference at 5:45 PM on May 28, 2011

Let's look at how Khan Academy is valuable.

Okay, let's say you want to learn quantum mechanics, but your not in college. It's not really the kind of thing one can just read a book on and understand it. There's a LOT of pre-requisites before you can even start to understand how it works.

Now, someone could start at the beginning, and systematically learn every single step along the way -- classical physics, statistical mechanics, calculus, calculus II, etc, etc. You can buy text books, you can go to college, etc. This will literally cost you 10s of thousands of dollars and take several years. And what if it turns out that you aren't cut out for it, or don't want to do it for a career, by the time you get to the level where you actually understand the course work?

With resources available on the internet (and Khan Academy is just one part of a broader phenomenon), you can start with quantum mechanics and work backwards.

Stanford has a bunch of lectures online by Leonard Susskind for free. Watch one. Let's say a few minutes into the first Quantum Mechanics course, he uses a derivative, and you've never done calculus before.

In just a few minutes, you can be at Khan Academy, start with wherever you feel comfortable with math and have him explain what derivatives are. You can go to wikipedia and read an article about derivatives and read an article about quantum mechanics, and see how the two are related. You can go to Wolfram Alpha, and plug in the numbers and actually see the equations worked out. If you like, you can even work out a bunch of problems yourself.

Then you go back to quantum mechanics, get stumped again and start the process all over.

This is not something theoretical, I've been doing exactly this for the past year or so, though I started with doing the Khan academy calculus videos on their own, they opened up a whole world of possibilities in terms of educating myself, because before, I never would have been able to pick up on this stuff on a whim. It would have been something I'd have had to dedicate several years of my life and a lot of money to, and I just don't have either to spare.

Now, am I learning this as well as someone with a university education? No. But am I learning it enough so that I can read new physics papers and understand them better than the average pop-sci journalist that writes about them in newspapers or blogs? I think probably so.posted by empath at 5:56 PM on May 28, 2011 [4 favorites]

If I tried to do this with one of my classes, they would revolt. They're there because the course is required for their major. What they want is to get through it as painlessly as possible. Why they should be required to learn algorithms performed as rituals with minimal understanding to get their degree is something I can't understand, and yet, that's how it is.

Right, and for some reason, none of the teachers in this thread see this as a problem with the way we educate people that can actually be addressed. They think that because they are told to think that, and they are told to think that because our educational system is fundamentally broken.posted by empath at 5:57 PM on May 28, 2011

none of the teachers in this thread see this as a problem with the way we educate people that can actually be addressed.

I didn't happen to mention it, but I do think this. It's just that thinking about this makes me contemplate the enormity of addressing this (basically we have to redesign All Of Education) and depresses the hell out of me, so I don't like to talk about it.posted by madcaptenor at 6:00 PM on May 28, 2011

It's just that thinking about this makes me contemplate the enormity of addressing this (basically we have to redesign All Of Education) and depresses the hell out of me, so I don't like to talk about it.

Well, you can redesign the Educational System, or you can just do what Khan did and go around it. I genuinely wish more teachers would do what he does. Khan Academy is great, but he's just one guy. He can't teach everything.posted by empath at 6:03 PM on May 28, 2011 [1 favorite]

I've thought of going around it. To be honest I'm not sure what's stopping me.posted by madcaptenor at 6:14 PM on May 28, 2011

I've thought of going around it. To be honest I'm not sure what's stopping me.

There is little doubt in my mind that we should have a very high number of our kids getting vocational training--perhaps as high as, say, 80%--rather than being taught in a system designed to produce scholars.

This is said more and more fequently these days, but what vocations would you train them in?posted by carping demon at 7:22 PM on May 28, 2011 [1 favorite]

I'm pretty sure the canonical example of vocation to train people in is plumber, because:

- there's no way you can do that remotely;
- when you need a plumber, you need a plumber;
- Mario and Luigi were plumbers.posted by madcaptenor at 7:30 PM on May 28, 2011

This is said more and more fequently these days, but what vocations would you train them in?

IT? There's still a shortage of people who know what they're doing, and in my experience, a degree doesn't help one bit for the vast majority of IT jobs.posted by empath at 8:03 PM on May 28, 2011 [2 favorites]

That's not the same thing.posted by empath at 10:21 PM on May 28, 2011

In math classes, it's always "what is this used for". Often, the answer is nothing.

The answer is almost never nothing, especially for high school math.

Nothing in Math is *useless*, but that's not the question most high school students ask. They ask "When are *we* going to use this?"

It's truthful to answer many (if not most) of them with "rarely" to "never," while some will use it occasionally, and some fewer will use what they're taught almost daily.

I completed a BS in Math, and I'm in the occasional group at best.

The problem is that most students (or people around them) don't know which group they're going to be a part of. That's pretty much what I told the students in my classes when I went on to have a go at a BA in Math Ed and ended up in a high school classroom. It didn't contain half the skepticism I came to have of the value of the curriculum and Math in general for most of the students, but it was probably the best thing to tell them.

With resources available on the internet (and Khan Academy is just one part of a broader phenomenon), you can start with quantum mechanics and work backwards.

This was more or less my central idea for changing the curriculum. Start with problems. Everybody seems to have an idea of how to reform things, though, and unlike me and thousands of other people, Khan has done something.posted by weston at 10:27 PM on May 28, 2011

I am motivated to practice math because....

For me, the area of high school math with the fewest obvious real-world applications was geometry. All those triangle formulas and those hours spent fiddling around with a straight edge and compass; I was never going to use any of that in the real world. Geometry seemed like the wading pool of mathematics—a shallow place to play for those unable to swim the deeper waters of linear algebra and calculus. I believe my high school geometry class was the least rigorous math course I have ever taken.

Imagine my surprise 12 years later when I found myself writing up a patent application for a chip largely devoted to calculating the Law of Cosines. That chip is a geometry powerhouse built for 3D graphics. It solves the Law of Cosines tens of billions of times per second. Today that chip is about to go to manufacturing. It is the primary product of a $30M tech startup.

Through the clever application of high school geometry, I have generated profit for my investors, created dozens of engineering jobs, secured several immigration visas, and earned hundreds of thousands of dollars for myself. All from triangles and straight edges!posted by ryanrs at 11:25 PM on May 28, 2011 [2 favorites]

One thing that I think has been touched on but not really elucidated is how valuable the Khan stuff is for non-traditional students. For obvious reasons, I think the upper end of the bell curve of math instructors tends to teach in traditional, prestigious settings, rather than community colleges, night programs, etc.

Just as a case in point - I'm re-taking a bunch of math courses to go to grad school (was humanities major in undergrad; was a mathphobe/didn't care when I took them the first time). I take classes at a night school. Before taking calculus 1 last fall, I had taken it two other times; once in college and once in high school. I watched the intro Khan video before this year's midterm, where he says something along the lines of "calculus is the study of change". No one had ever explained that concept to me before, it was all wrote memorization of meaningless algorithms. It was one of those lightning bolt moments; I aced the class.

The Khan model doesn't have to mean the end of education as we know it, or anything like that, it's just that he's found a way to scale the effective pedagogical techniques of the upper end of the math teacher distribution. That can be a huge deal without deep ramifications for education models.posted by downing street memo at 11:40 PM on May 28, 2011 [1 favorite]

I think the upper end of the bell curve of math instructors tends to teach in traditional, prestigious settings, rather than community colleges, night programs, etc.

While I don't doubt that this is true, my calculus instructors at Portland Community College (Sylvania) were honestly the best teachers I've ever had (from small liberal-arts college to big state research university). Some fantastic teachers self-select into the community college system because they love being able to focus exclusively on teaching.posted by dialetheia at 11:52 PM on May 28, 2011

I once heard about a famous journalist who taught a class in college. At the beginning of the first meeting, he announced that everybody would get a B (this was in the pre-grade-inflation days when a B was a pretty good grade).

The gradeholic students who were after As instead of after knowledge dropped the class, and the stupid and lazy students thought "hey, easy B" and stopped coming to class. So, very soon, the class consisted entirely of students who wanted to learn about journalism. He drove them very hard and, I'm sure, gave all of them something that they kept for their whole life.

While I'd love to be able to pull a stunt like this (I teach math in college), the moral of the story for me is that in order to teach math to students, you first need to make them care about learning math. That means you need to explain what math is (they don't know -- worse, they think they know) and what it can do. Only then will they find enough motivation to sit down and think hard.posted by pguertin at 12:11 AM on May 29, 2011

What is it used for! Give me a break. They never teach you any math that isn't used all the time by working people until you get to university, true - but the fact is that learning logical reasoning and numerical skills intrinsically makes you a better and stronger person, even if you're learning something that has no real-world applications.

But, let's be clear: my gripe is not about innovation or having online videos. It's about the fact that a rich outsider hobbyist comes along doing things that many, many, MANY, educators already do, and somehow he's some sort of great education innovator. He's not.

So if I want to get an educator to deliver a lecture on a subject, right now, for free, and then immediately test me on that subject, I could do that? And then I could get immediate feedback from other students if I have questions about the subject that were addressed in the lecture? Where are these educators exactly?posted by runcibleshaw at 12:56 AM on May 29, 2011 [1 favorite]

I still don't know what a matrix is or what it represents

Matrices can represent lots of different things, depending on what they're being used for. A matrix is just a convenient way to organize a bunch of numbers that are related to each other.

I know you're trying to help, but this is a bit like saying "a matrix is a matrix of things that you put into a matrix".

I guess my question would be, uh, why? Why are the things put in a matrix in the first place? What determines the order the things are in, or the size and shape of the matrix? Why are matrices rectangular and not triangles or rhombuses? I understand that they're very useful when it comes to working on the math involved in general relativity, but surely there's some other more basic application. Like, I have 12 numbers, why would I put them in this weird box?posted by runcibleshaw at 1:05 AM on May 29, 2011

Ever use a spreadsheet? Matrices are kind of like that. Say you have ten objects that can each be described using three numeric properties. You might represent this as a matrix with three columns and ten rows. Matrices are more general than that, but that's a good start.posted by ryanrs at 4:24 AM on May 29, 2011

What other theory were you talking about?

Modern theoretical physics. All particles and fields are mathematical objects. There's nothing to them that isn't math.posted by empath at 5:59 AM on May 29, 2011

"When was the last time you actually multiplied two large numbers by hand, or divided two fractions?"

???

I do it all the time at work because scribbling on a Post-It is faster than mousing and clicking my way through Start > Programs > Accessories > Calculator. Also, when I do it by hand I don't have to worry about mistyping a number, or accidentally hitting the wrong button and clearing the results of an intermediate calculation before I'm done with what I'm figuring out. So in my experience, doing these sorts of basic arithmetic calculations are much quicker, easier, and accurate when I do them by hand than when I do them by calculator.

Am I just a total weirdo in this regard?

(I also usually forget to bring a calculator to exams, and thus turn them with long columns of tiny long division calculations running down the margins like some sort of decorative fringe for the "show your work" space that is only ever big enough to show one's work if one is using a calculator for all the arithmetic. Sigh.)posted by Jacqueline at 6:29 AM on May 29, 2011 [1 favorite]

On the other hand, I had an employee who claimed that she was "really good at math, except division" (she didn't know how to divide). She genuinely, sincerely believed that math was only arithmetic and that by mastering addition, subtraction, and multiplication that she had learned most of what "math" was. She was a high school graduate and in her mid-20s yet no one had ever disabused her of this notion.

I always assumed that she was probably just mildly retarded and had maybe graduated from some sort of special ed program but after reading this thread I'm beginning to wonder whether she is closer to the norm than I am?posted by Jacqueline at 6:38 AM on May 29, 2011

There's nothing to them that isn't math.

The physical world has nothing to do with math. Your model may be made of math, but then again, models usually are. It's kind of like saying people are made of math, since population statistics are based on math. Of course, math won't tell you anything about any particular person, but modern quantum theories suffer from a similar deficiency.posted by ryanrs at 6:45 AM on May 29, 2011

On the other other hand, my engineer coworkers make me feel retarded because whenever something comes up in conversation that would require a quick series of arithmetic calculations they get to the answer in their head before I can even get out my Post-Its.

(For those of you wondering what the fuck it is that I do for a living that requires so much spontaneous arithmetic, mostly we're either discussing salary charges that need to be multiplied by a fringe rate then an overhead rate to figure out the final total, or discussing a budget amount that we need to divide by the overhead rate and then the fringe rate to figure out how much we have left to spend on a project. Perhaps they're so fast at it just because they have 8 years' more experience than I have in multiplying and dividing specifically by the numbers 1.42 and 1.69, LOL!)posted by Jacqueline at 6:47 AM on May 29, 2011

The physical world has nothing to do with math.

I really can't disagree with this more. Once you get down to the level of quantum field theory and individual particles and strings, no physical interpretation makes sense. It only makes sense if you treat them purely as mathematical objects.posted by empath at 6:54 AM on May 29, 2011

Ah, 1.42, my good friend! Jacqueline, the trick to dividing by 1.42 is recognizing that it is the square root of 2 (pretty much). Therefore you can easily swap your division for multiplication:
x / 1.42 = x * 1.42 / 2

There isn't such a cute trick for 1.69, as far as I can see. You can divide by 13 twice, I guess.posted by ryanrs at 6:57 AM on May 29, 2011 [1 favorite]

Empath, you're mistaking the model for the thing itself. If you're willing to do that, then you can say anything is "made of math" since models are generally mathematical in nature.posted by ryanrs at 6:59 AM on May 29, 2011

> Empath, you're mistaking the model for the thing itself.

Um, perhaps you're the one who's mistaken. What exactly is the universe made of? Electrons, photos, that sort of thing, but what are they? As we get down to the parts, we get down to tiny pieces that have very limited abstract behavior and otherwise make little or no intuitive sense. Many philosophers of science have speculated as a result that the universe is, in fact, made up of mathematics.

> If you're willing to do that, then you can say anything is "made of math" since models are generally mathematical in nature.

Not so. For more complex things like "a dog" a mathematical model is neither complete nor completely predictive. Only when you get to tiny things like sub-atomic particles do you see things that look and behave nothing like "real world" objects we're used to, and much more like perfect, abstract mathematical things.posted by lupus_yonderboy at 7:56 AM on May 29, 2011

"With resources available on the internet (and Khan Academy is just one part of a broader phenomenon), you can start with quantum mechanics and work backwards... [gives example]"

The general strategy that empath describes is exactly how I am able to copyedit scientific journal articles despite having almost no science background (I was an econ major). I am basically "working backwards" on almost all my on-the-job reading.

Scenario: I get a paper to edit in which the author apparently thought of what he/she wanted to say in Chinese and then just translated it into English word-for-word without bothering to change the syntax. Since it's also in a technical field I know nothing about, not only do I have the usual WTF Chinglist word salad issues to deal with but I also have no background knowledge of the terminology to clue me in as to where the compound adjectives end and the compound nouns begin.

So it's off to Wikipedia to look each term up one-by-one until I figure out how they logically relate to one another and thus can rewrite the sentence so that it says what the author meant for it to say. Or if they're citing another paper, it's off to Google Scholar for the abstract (which thankfully I can usually count on having been edited by a native English speaker) to make sure that the paper they're citing actually says what it is I think they're claiming it says.

I literally could not do my job if it weren't for these internet resources. So I think it's a pretty fucking amazing technological accomplish that the internet enables someone like me to edit stuff like that.posted by Jacqueline at 7:57 AM on May 29, 2011 [1 favorite]

*accomplishment

Sigh... it seems to be a law of the universe that I can't write a comment ragging on someone else's writing skills without making a blatantly stupid error myself.posted by Jacqueline at 8:02 AM on May 29, 2011

For more complex things like "a dog" a mathematical model is neither complete nor completely predictive.

You could model the size of a dog, its mass, lifespan, and all sorts of other things. Completeness and complete predictiveness are unnecessary.

Mostly though, I'm just pissing on modern physics. I find those models so useless compared to classical mechanics and other high school fare. What interesting thing have you ever predicted using modern physics? Bringing it up to justify high school math doesn't seem right.posted by ryanrs at 8:21 AM on May 29, 2011

But the thing is, the various resources you're using still don't do a great job of providing motivation, of telling you why you'd want to learn these things. Since you already have the motivation -- some particular task you're trying to accomplish -- that's not a problem. Some of the criticism is that Khan doesn't solve that problem, and therefore is not a silver bullet, but is being touted as such.posted by madcaptenor at 10:09 AM on May 29, 2011

It only makes sense if you treat them purely as mathematical objects.

This is Tegmark's the-universe-is-math theory, which has the criticisms I referred to earlier.posted by Blazecock Pileon at 12:38 PM on May 29, 2011

See An Open Letter to Sal Khan, from the Mathalicious company blog. Mathalicious is the company of Karim Ani, a former math teacher who's started a company that is "rewriting the math curriculum around real-world topics". Basically, he's saying that Khan is doing good work (with the criticism that "Socrates didn't wing it") but finds whole Khan-as-messiah-of-education thing is overblown. This is in response to this Washington Post column by Steven Pearlstein, saying that with the combination of the Internet, ridiculously high tuition and textbook prices, and growing discontent, perhaps we will in fact see some sort of revolution in education. (But haven't we heard this before?)posted by madcaptenor at 1:00 PM on May 29, 2011 [2 favorites]

As others have said, I tremendously wish I knew about this guy when I was in college because I would have done A LOT better in math if I had access to him.posted by champthom at 5:17 AM on May 30, 2011

the various resources you're using still don't do a great job of providing motivation

> What interesting thing have you ever predicted using modern physics?

It depends on what you mean by "modern" physics, I suppose, but semiconductor physics relies on quantum mechanics and without it, we wouldn't have computer chips, the internet, or Metafilter...posted by lupus_yonderboy at 3:59 PM on May 30, 2011 [2 favorites]

I've been going through some of the pretty basic practice exercises. As someone who was not super into math in school and just viewed it as a nuisance to get over with as soon as possible, it is quite helpful to be able to refresh basic skills at my convenience, with help available.

I do think, though, that's it's pretty ironic to be reviewing basic math on a scratchpad sent to me by my college's alumni association.posted by ghharr at 9:00 PM on June 2, 2011

Is there a Khan Academy for learning Python/Ruby/Perl?posted by mecran01 at 9:16 PM on June 3, 2011

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